Introduction to Probability phần 3 pptx

... 0.9 237 329294 6 0.6 135 495966 7 0 .33 40609995 8 0.1671586419 9 0.0854201 934 10 0.0429455489 11 0.02150 237 60 12 0.0107548 935 13 0.00 537 79101 14 0.0026890 130 Table 3. 14: Distance to the random process. 5 ... (1994), pp. 30 3 33 1. 29 D. Bayer and P. Dia coni s, “Trailing the Dovetail Shuffle to its Lair,” Annals of Applied Prob- ability, vol. 2, no. 2 (1992), pp. 294 31 3....

Ngày tải lên: 09/08/2014, 23:20

... Experiments with Feedback to Sub- jects,” Annals of Statistics, vol. 9 (1981), pp. 3 23. 6.2. VARIANCE OF DISCRETE RANDOM VARIABLES 261 1 2 3 4 5 6 0 0.1 0.2 0 .3 0.4 0.5 0.6 2 2.5 3 3.5 4 4.5 5 0 0.5 1 1.5 2 n ... the numbers 1 to 36 marked on equal slots; the wheel is spun and a ball stops randomly in one slot. When a player bets 1 dollar on a number, he receives 36 dollars if...

Ngày tải lên: 09/08/2014, 23:20

... {a 1 ,a 2 ,a 3 ,a 4 } can be written in the form σ =  1 234 21 43  , indicating that a 1 went to a 2 , a 2 to a 1 , a 3 to a 4 , and a 4 to a 3 . Ifwealwayschoosethetoprowtobe1 234 then, to prescribe ... ω 2 , ω 3 , and ω 5 . Each of these paths has the same probability p 2 q.Thusb (3, p,2)=3p 2 q. Considering all possible numbers of successes we have b (3, p,0) = q 3...

Ngày tải lên: 04/07/2014, 10:20

... vol. 204 (1 937 ), pp. 39 7 39 9. 7.1. SUMS OF DISCRETE RANDOM VARIABLES 287 = 1 36 · 1 6 = 1 216 , P (S 3 =4) = P(S 2 =3) P (X 3 =1)+P (S 2 =2)P (X 3 =2) = 2 36 · 1 6 + 1 36 · 1 6 = 3 216 , and ... (S 2 =8)=5 /36 , P (S 2 =9)=4 /36 , P (S 2 =10) =3/ 36, P (S 2 =11)=2 /36 , and P(S 2 =12)=1 /36 . The distribution for S 3 would then be the convolution of the distribution fo...

Ngày tải lên: 04/07/2014, 10:20

... BRANCHING PROCESSES 38 3 Generation Probability of dying out 1.2 2 .31 2 3 .38 52 03 4 . 437 116 5 .475879 6 .505878 7 .5297 13 8 .549 035 9 .564949 10 .578225 11 .589416 12 .598 931 Table 10.1: Probability of ... -50 000000000000-100 11111124979 730 0 233 420000000 0 100000000000 -50 210000000000 0 33 471117141111101625 130 0 000000000000-100 1221 131 00000 -50 000000000000-100...

Ngày tải lên: 04/07/2014, 10:20

... -200 up H 28.8 25 to 200 2 O 29.4 25 to 200 2 H O(g)* 36 .4 25 to 200 2 SO (g) 41.9 25 to 200 2 S (r) 23. 7 25 to 200 S (m) 25.9 95 to 120 *For rough calculations it is sufficient to set C (steam) ... the reaction. (5) T q dS rev = KJ/g 22.1 K 15.2 73 J/g 6 .33 3 ⋅===∆ T Q S rev KJ/g 22.1 K 15.2 73 (ice) J/g 6 .33 3 ⋅−= − =∆ thermostat S 7/10/07 2- 37 (T) ∆A = W (4) rev T...

Ngày tải lên: 08/08/2014, 15:21

... consider. Have a look at the Customer and Email classes defined in Listing 5 -3. Listing 5 -3. Customer and Email Classes public class Customer { int customerId; int customerReference; String name; Email ... set to 10 • Two rows for the user, with both ages set to 10 • Two rows for the user, with one age set to 10 and the other to 42 • Two rows for the user, with one age set to 10...

Ngày tải lên: 09/08/2014, 14:20

... = 1/4 1 −1/4 = 1 3 . Thus the probability that a head turns up for the first time after an even number of tosses is 1 /3 and after an odd number of tosses is 2 /3. ✷ 8 CHAPTER 1. DISCRETE PROBABILITY ... of the exercises is available to instructors. Historical remarks: Introductory probability is a subject in which the funda- mental ideas are still closely tied to those of the fou...

Ngày tải lên: 09/08/2014, 23:20

... 5000 2 532 3. 1596 Smith, 1855 .6 32 04 1218.5 3. 15 53 De Morgan, c.1860 1.0 600 38 2.5 3. 137 Fox, 1864 .75 1 030 489 3. 1595 Lazzerini, 1901 . 83 3408 1808 3. 1415929 Reina, 1925 .5419 2520 869 3. 1795 Table ... 1.011 8 4 032 0 39 902 .39 5 1.010 9 36 2880 35 9 536 .8 73 1.009 10 36 28800 35 98696.619 1.008 Table 3. 4: Stirling approximations to the factorial function....

Ngày tải lên: 09/08/2014, 23:20

... .9048 .36 79 .36 60 .0000 .0000 1 .0905 .0905 .36 79 .36 97 .0005 .0004 2 .0045 .0045 .1 839 .1849 .00 23 .0022 3 .0002 .0002 .06 13 .0610 .0076 .0074 4 .0000 .0000 .01 53 .0149 .0189 .0186 5 .0 031 .0029 ... . 037 8 . 037 4 6 .0005 .0005 .0 631 .0627 7 .0001 .0001 .0901 .0900 8 .0000 .0000 .1126 .1128 9 .1251 .1256 10 .1251 .1257 11 .1 137 .11 43 12 .0948 .0952 13 .0729 .0 731 14 .0...

Ngày tải lên: 09/08/2014, 23:20